Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops

TL;DR

This paper addresses a key issue in the CGC/saturation approach by demonstrating that pion loop summation causes an exponential decay of scattering amplitudes at large impact parameters, restoring theoretical consistency with the Froissart theorem.

Contribution

It introduces a novel solution to the large impact parameter problem in the CGC/saturation framework through pion loop summation, ensuring amplitudes decay exponentially.

Findings

Pion loops lead to exponential fall of scattering amplitudes at large impact parameters.

Restoration of the Froissart theorem in the CGC/saturation approach.

Addresses longstanding inconsistency in high-energy QCD models.

Abstract

In this paper we proposed a solution to the longstanding problem of the CGC/saturation approach: the power-like fall of the scattering amplitudes at large $b$. This decrease leads to the violation of the Froissart theorem and makes the approach theoretically inconsistent. We showed in the paper that sum of the pion loops results in the exponential fall of the scattering amplitude at large impact parameters and in the restoration of the Froissart theorem.